View source for Network Planning in Project Management

==Abstract==
Planning is a big part of project management, and the success of it is highly dependent on this process. The method Network planning will be used to reduce possible complexity of a project and smoothen the execution of the project planning. A project of a large scale that require coordination of multiple activities is a challenging task for a project manager. Succeeding a project is about simple forms of working and organising <ref name="DP"/> regardless of the size of the project. The method will therefore be used as an integration approach where the different activities are separated to get an overview of the process. Understanding the dependencies of the project and setting up millstones is also ideal to motivate the employees involved in the project.

Project networking is investigating a project as sets of interconnected activities with the purpose of assisting in planning, managing, and controlling projects <ref name="NW"/>. This article will mainly focus on the most well know network planning techniques: the Critical path method (CPM) and the Program evaluation and review technique (PERT). CPM and PERT was developed in the 1950’s and has since then been used widely in operation research <ref name="OR"/>.  The goal of the tool is to manage a project, meeting its deadlines with a minimum total cost. The tools will help organising the project, getting an overview of the activities and estimate the total length of the project. There can be multiple paths to the end of the project, but those tools can help the manager find the most effective one. Initially the methods will need three types of information to describe the project: activity, precedence, and time <ref name="OR"/>. This will be elaborated in the article followed by a description of the tool, an example of how to use the tool, other alternative planning tools and the limitations of the tool.

This article will elaborate the theory behind network/graphs and the focus on the comparison of different planning tools that are not focused on network planning specifically. The article is based on a project managers point of view and what that person may consider and wonder about when planning a project.

==Network Theory==

The first section will describe the terminology of network planning.

===Graph Theory===

A graph that consists of multiple nodes and arcs are considered a network. This means that a network consists of nodes that are connected through arcs. In this article the exploration of networks will be centered around project planning, which means that the nodes correspond to the events in the project. The arcs correspond to the connection between the events and can be either directed or undirected. When an arc is directed, for example for A to B, it means that the network can only go from A to B and not from B to A.
An example of a network is illustrated below.

[[File:Spanning_Tree.png  |thumb|420px|right| Figure 1]]

====Spanning Tree====

Consider a network with a number of nodes ''n'' and no initially arcs. By adding one arc at a time between the nodes, a tree will appear. The first arc can be between any of the nodes in the network, but along the way, an arc cannot be placed if it creates a cycle. A network of nodes connected through arcs are referred to as a spanning tree. A network therefore differs between being cyclic or acyclic

==CPM/PERT==

The CPM/PERT method is an ideal too to get an overview of a project planning process and help answering multiple questions that a project manager may have for the process. 

====Initial work====
As mentioned earlier, some information is needed in order to use network theory for planning a project:

1. Activity information: the project must be broken down into individual activities

2. Precedence relationships: find immediate predecessor(s) for each activity

3. Time information: know/estimate the duration of each activity

Other than that, a network will have one or more start node(s) and a finish node/node(s).

A project network can be split into two, depending on whether the activity is on the node or on the arc. Those two types are referred to ''Activity-on-arc'' (AOA) and ''Activity-on-node'' (AON). For the AOA, the node is separating the activities and therefor the arcs show the precedence relationship between the activities on the nodes. The AON is used in the CPM/PERT that will be elaborated later in this article. The AON method is remarkable more simpel to construct, understand and revise than the AOA. Therefor this article will forward going only focus on AON.

====Critical Path====
The critical path is a part of the project planning method that can answer how long time the project will take to complete and what are the bottlenecks to be aware of in order to prevent delays of the whole project?

The critical path will establish the time length of the project, summing over all the durations of the activities. In a project network from a starting node to an end node, multiple paths can be set up if the activities can be done in sequence with a predecessors and no overlap. Therefor some activities have to wait for other activities to finish before it can start. Those can be activities that are on another path. 
The path with the longest total duration time is the critical path and therefor the longest duration time that the project can take assuming no delays occur. This is also the bottleneck activities of the project where delays most be avoided so that the whole project can be completed in time. 

====Scheduling====

==CPM/PERT Example==

==Further research on the method==

This article is narrowed down to only looking at the time aspect of project network planning, but there is more of the tool to investigate. The method may be expanded to uncertainty and costs which are also very important aspects of project planning. 

The method is using accurate estimations of activity duration, which is associated with some uncertainty. Therefor it is very relevant for the project manager to know what the probability is to meet the deadline. The uncertainty is then expanded to include time-costs trade offs. So if it possible to decrease uncertainty with increased cost.

This part of the method will not be further investigated in this article.


==Limitations==
Going through the possible questions of a project manager, this tool is indeed a great tool to answer the questions represented in this article. On the other hand, this tool does have some limitations to be aware of. The tool is great to visualise those small examples, but it will be more difficult to use it with big complex projects where the time estimations and predecessors are hard to identify. It can rapidly become a very time consuming task to draw up the diagram and make the scheduling calculations for every activity. To solve this on larger problems, you may have to use linear programming, but that can also be very complex and time consuming to set up.

It is a very simple method, which makes is great to answer the questions that are asked in this article, but there is also a lot of other questions that the method does no answer. It i focused on the time aspect, but not on any resources of the project. This is causing a lot of inflexibility for the process and may not work on the longer term projects.

== Alternative planning tools==

Since all project planning tools have pros and cons, this method may be more relevant for some projects and some other methods may work for the other projects. Other examples of project planning tools are [[Gantt Charts]] and [[Milestone Planning]].

If the project manager wants to get a better overview of the resources in a project, which the CPM/PERT does not include, the [[Gantt Charts]] is a great alternative. With the [[Gantt Charts]] it is easy to follow how the resources are utilised.
The [[Milestone Planning]] method is a great reactive tool to evaluate on the progress of the project. At the same time, this tool seems more simple than the CPM/PERT and would therefor be easier to use on big projects.

==References==
<references>

<ref name="OR"> Retrieved from F. S. Hillier & G. J. Lieberman. (2015). Introduction to operation research. </ref>

<ref name="DP"> Retrieved from J. Geraldi, C. Thuesen, & J. Oehmen. (2017). Doing Projects - Nordic flavour to managing projects. </ref>

<ref name="NW"> Retrieved from Rand, Graham K. & Tavares, Luis Valadares. (2005). Network Planning: Encyclopedia of Operations Research and Management Science. </ref>